Question

The three angles of a triangle are in the ratio 1:2:3 Find the measure of each angle
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Answer 1

Answer:

Let the angles be x, 2x and 3x

Sum of the triangle =180 degree

x+2x+3x=180

6x=180

x=180/6

x=30

First angle =30

Second angle =2*30=60

Third angle =3*30=90

Step-by-step explanation:

Answer 2

Given:-

• Ratio of angles of a triangle = 1:2:3

To find:-

Angles of the triangle

Assumption:-

Let the common multiple of the ratios be x

• 1st angle = 1x
• 2nd angle = 2x
• 3rd angle = 3x

Solution:-

According to the angle-sum property of a triangle

$\sf{1x + 2x + 3x = 180^\circ}$

=> $\sf{6x = 180^\circ}$

=> $\sf{x = \dfrac{180^\circ}{6}}$

=> $\sf{x = 30^\circ}$

Now,

Measures of each angles:-

$\sf{1st\: angle = 1x = 1 \times 30^\circ = 30^\circ}$

$\sf{2nd\: angle = 2x = 2\times 30^\circ = 60^\circ}$

$\sf{3rd\:angle = 3x = 2\times 30^\circ = 90^\circ}$

Extra information:-

-> What is angle-sum property of a triangle?

Ans - Angle-Sum property of a triangle states that the sum of all the angles of a triangle is always 180°